期刊
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
卷 21, 期 3, 页码 379-394出版社
WALTER DE GRUYTER GMBH
DOI: 10.1515/jip-2013-0002
关键词
Tikhonov regularisation; convergence rates; variational inequalities; duality mappings; Bregman distance
In this paper we derive higher order convergence rates in terms of the Bregman distance for Tikhonov like convex regularisation for linear operator equations on Banach spaces. The approach is based on the idea of variational inequalities, which are, however, not imposed on the original Tikhonov functional, but rather on a dual functional. Because of that, the approach is not limited to convergence rates of lower order, but yields the same range of rates that is well known for quadratic regularisation on Hilbert spaces.
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